Material Properties and Residual Stress in the Stage 12 Chick Heart During Cardiac Looping

Stress sharing as cognitive glue for collective intelligences: A computational model of stress as a coordinator for morphogenesis

Individual cells have numerous competencies in physiological and metabolic spaces. However, multicellular collectives can reliably navigate anatomical morphospace towards much larger, reliable endpoints. Understanding the robustness and control properties of this process is critical for evolutionary developmental biology, bioengineering, and regenerative medicine. One mechanism that has been proposed for enabling individual cells to coordinate toward specific morphological outcomes is the sharing of stress (where stress is a physiological parameter that reflects the current amount of error in the context of a homeostatic loop). Here, we construct and analyze a multiscale agent-based model of morphogenesis in which we quantitatively examine the impact of stress sharing on the ability to reach target morphology. We found that stress sharing improves the morphogenetic efficiency of multicellular collectives; populations with stress sharing reached anatomical targets faster. Moreover, stress sharing influenced the future fate of distant cells in the multi-cellular collective, enhancing cells' movement and their radius of influence, consistent with the hypothesis that stress sharing works to increase cohesiveness of collectives. During development, anatomical goal states could not be inferred from observation of stress states, revealing the limitations of knowledge of goals by an extern observer outside the system itself. Taken together, our analyses support an important role for stress sharing in natural and engineered systems that seek robust large-scale behaviors to emerge from the activity of their competent components.

Quantifying Spatial Patterns of Tissue Stiffness Within the Embryonic Mouse Kidney

Biophysical factors, including changes in mechanical stiffness, have been shown to influence the morphogenesis of developing organs. There is a lack of experimental techniques, however, that can probe the mechanical properties of embryonic tissues-especially those which are not mechanically or optically accessible, such as the visceral organs of the developing mouse embryo. Here, using the embryonic kidney as a model system, we describe a method to use microindentation to quantify tissue-level regional differences in the mechanical properties of an embryonic organ. This technique is generalizable and can be used to quantify patterns of tissue stiffness within other developing organ systems. Going forward, these data will enable new experimental studies of the role of biophysical cues during organogenesis.

Evo-Devo Mechanobiology: The Missing Link

While the modern framework of evolutionary development (evo-devo) has been decidedly genetic, historic analyses have also considered the importance of mechanics in the evolution of form. With the aid of recent technological advancements in both quantifying and perturbing changes in the molecular and mechanical effectors of organismal shape, how molecular and genetic cues regulate the biophysical aspects of morphogenesis is becoming increasingly well studied. As a result, this is an opportune time to consider how the tissue-scale mechanics that underlie morphogenesis are acted upon through evolution to establish morphological diversity. Such a focus will enable a field of evo-devo mechanobiology that will serve to better elucidate the opaque relations between genes and forms by articulating intermediary physical mechanisms. Here, we review how the evolution of shape is measured and related to genetics, how recent strides have been made in the dissection of developmental tissue mechanics, and how we expect these areas to coalesce in evo-devo studies in the future.

Targeted mechanical stimulation via magnetic nanoparticles guides in vitro tissue development

Tissues take shape through a series of morphogenetic movements guided by local cell-scale mechanical forces. Current in vitro approaches to recapitulate tissue mechanics rely on uncontrolled self-organization or on the imposition of extrinsic and homogenous forces using matrix or instrument-driven stimulation, thereby failing to recapitulate highly localized and spatially varying forces. Here we develop a method for targeted mechanical stimulation of organoids using embedded magnetic nanoparticles. We show that magnetic clusters within organoids can be produced by sequential aggregation of magnetically labeled and non-labeled human pluripotent stem cells. These clusters impose local mechanical forces on the surrounding cells in response to applied magnetic fields. We show that precise, spatially defined actuation provides short-term mechanical tissue perturbations as well as long-term cytoskeleton remodeling in these organoids, which we term "magnetoids". We demonstrate that targeted magnetic nanoparticle-driven actuation guides asymmetric tissue growth and proliferation, leading to enhanced patterning in human neural magnetoids. This approach, enabled by nanoparticle technology, allows for precise and locally controllable mechanical actuation in human neural tube organoids, and could be widely applicable to interrogate the role of local mechanotransduction in developmental and disease model systems.

Embryonic aortic arch material properties obtained by optical coherence tomography-guided micropipette aspiration

It is challenging to determine the in vivo material properties of a very soft, mesoscale arterial vesselsof size ∼ 80 to 120 μm diameter. This information is essential to understand the early embryonic cardiovascular development featuring rapidly evolving dynamic microstructure. Previous research efforts to describe the properties of the embryonic great vessels are very limited. Our objective is to measure the local material properties of pharyngeal aortic arch tissue of the chick-embryo during the early Hamburger-Hamilton (HH) stages, HH18 and HH24. Integrating the micropipette aspiration technique with optical coherence tomography (OCT) imaging, a clear vision of the aspirated arch geometry is achieved for an inner pipette radius of Rp = 25 μm. The aspiration of this region is performed through a calibrated negatively pressurized micro-pipette. A computational finite element model is developed to model the nonlinear behaviour of the arch structure by considering the geometry-dependent constraints. Numerical estimations of the nonlinear material parameters for aortic arch samples are presented. The exponential material nonlinearity parameter (a) of aortic arch tissue increases statistically significantly from a = 0.068 ± 0.013 at HH18 to a = 0.260 ± 0.014 at HH24 (p = 0.0286). As such, the aspirated tissue length decreases from 53 μm at HH18 to 34 μm at HH24. The calculated NeoHookean shear modulus increases from 51 Pa at HH18 to 93 Pa at HH24 which indicates a statistically significant stiffness increase. These changes are due to the dynamic changes of collagen and elastin content in the media layer of the vessel during development.

Following the Beat: Imaging the Valveless Pumping Function in the Early Embryonic Heart

In vertebrates, the coordinated beat of the early heart tube drives cardiogenesis and supports embryonic growth. How the heart pumps at this valveless stage marks a fascinating problem that is of vital significance for understanding cardiac development and defects. The developing heart achieves its function at the same time as continuous and dramatic morphological changes, which in turn modify its pumping dynamics. The beauty of this muti-time-scale process also highlights its complexity that requires interdisciplinary approaches to study. High-resolution optical imaging, particularly fast, four-dimensional (4D) imaging, plays a critical role in revealing the process of pumping, instructing numerical modeling, and enabling biomechanical analyses. In this review, we aim to connect the investigation of valveless pumping mechanisms with the recent advancements in embryonic cardiodynamic imaging, facilitating interactions between these two areas of study, in hopes of encouraging and motivating innovative work to further understand the early heartbeat.

Stiffness estimation of transversely anisotropic materials using a novel indentation tester with a rectangular hole

Since embryos change their morphology drastically in the gastrulation stage, mechanical characterization of young embryos is important as they also change their tissue stiffness with the stage of development. Herein, virtual compression tests were conducted assuming that the Xenopus laevis gastrula has a spherical shape with transverse anisotropy. Based on the design of experiments, we found that the Young's moduli and material anisotropy can be efficiently determined by measuring the reaction force and surface displacement when indenting the tester into an embryo. The proposed scheme may be a substantial step toward understanding the timing of cell-type specification during embryo development.

Soft-Tissue Material Properties and Mechanogenetics during Cardiovascular Development

During embryonic development, changes in the cardiovascular microstructure and material properties are essential for an integrated biomechanical understanding. This knowledge also enables realistic predictive computational tools, specifically targeting the formation of congenital heart defects. Material characterization of cardiovascular embryonic tissue at consequent embryonic stages is critical to understand growth, remodeling, and hemodynamic functions. Two biomechanical loading modes, which are wall shear stress and blood pressure, are associated with distinct molecular pathways and govern vascular morphology through microstructural remodeling. Dynamic embryonic tissues have complex signaling networks integrated with mechanical factors such as stress, strain, and stiffness. While the multiscale interplay between the mechanical loading modes and microstructural changes has been studied in animal models, mechanical characterization of early embryonic cardiovascular tissue is challenging due to the miniature sample sizes and active/passive vascular components. Accordingly, this comparative review focuses on the embryonic material characterization of developing cardiovascular systems and attempts to classify it for different species and embryonic timepoints. Key cardiovascular components including the great vessels, ventricles, heart valves, and the umbilical cord arteries are covered. A state-of-the-art review of experimental techniques for embryonic material characterization is provided along with the two novel methods developed to measure the residual and von Mises stress distributions in avian embryonic vessels noninvasively, for the first time in the literature. As attempted in this review, the compilation of embryonic mechanical properties will also contribute to our understanding of the mature cardiovascular system and possibly lead to new microstructural and genetic interventions to correct abnormal development.

An integrative multiscale view of early cardiac looping

The heart is the first organ to form and function during the development of an embryo. Heart development consists of a series of events believed to be highly conserved in vertebrates. Development of heart begins with the formation of the cardiac fields followed by a linear heart tube formation. The straight heart tube then undergoes a ventral bending prior to further bending and helical torsion to form a looped heart. The looping phase is then followed by ballooning, septation, and valve formation giving rise to a four-chambered heart in avians and mammals. The looping phase plays a central role in heart development. Successful looping is essential for proper alignment of the future cardiac chambers and tracts. As aberrant looping results in various congenital heart diseases, the mechanisms of cardiac looping have been studied for several decades by various disciplines. Many groups have studied anatomy, biology, genetics, and mechanical processes during heart looping, and have proposed multiple mechanisms. Computational modeling approaches have been utilized to examine the proposed mechanisms of the looping process. Still, the exact underlying mechanism(s) controlling the looping phase remain poorly understood. Although further experimental measurements are obviously still required, the need for more integrative computational modeling approaches is also apparent in order to make sense of the vast amount of experimental data and the complexity of multiscale developmental systems. Indeed, there needs to be an iterative interaction between experimentation and modeling in order to properly find the gap in the existing data and to validate proposed hypotheses. This article is categorized under: Cardiovascular Diseases > Genetics/Genomics/Epigenetics Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiology.

A model for 3D deformation and reconstruction of contractile microtissues

Tissue morphogenesis and regeneration are essentially mechanical processes that involve coordination of cellular forces, production and structural remodeling of extracellular matrix (ECM), and cell migration. Discovering the principles of cell-ECM interactions and tissue-scale deformation in mechanically-loaded tissues is instrumental to the development of novel regenerative therapies. The combination of high-throughput three-dimensional (3D) culture systems and experimentally-validated computational models accelerate the study of these principles. In our previous work [E. Mailand, et al., Biophys. J., 2019, 117, 975-986], we showed that prominent surface stresses emerge in constrained fibroblast-populated collagen gels, driving the morphogenesis of fibrous microtissues. Here, we introduce an active material model that allows the embodiment of surface and bulk contractile stresses while maintaining the passive elasticity of the ECM in a 3D setting. Unlike existing models, the stresses are driven by mechanosensing and not by an externally applied signal. The mechanosensing component is incorporated in the model through a direct coupling of the local deformation state with the associated contractile force generation. Further, we propose a finite element implementation to account for large deformations, nonlinear active material response, and surface effects. Simulation results quantitatively capture complex shape changes during tissue formation and as a response to surgical disruption of tissue boundaries, allowing precise calibration of the parameters of the 3D model. The results of this study imply that the organization of the extracellular matrix in the bulk of the tissue may not be a major factor behind the morphogenesis of fibrous tissues at sub-millimeter length scales.

Of form and function: Early cardiac morphogenesis across classical and emerging model systems

The heart is the earliest organ to develop during embryogenesis and is remarkable in its ability to function efficiently as it is being sculpted. Cardiac heart defects account for a high burden of childhood developmental disorders with many remaining poorly understood mechanistically. Decades of work across a multitude of model organisms has informed our understanding of early cardiac differentiation and morphogenesis and has simultaneously opened new and unanswered questions. Here we have synthesized current knowledge in the field and reviewed recent developments in the realm of imaging, bioengineering and genetic technology and ex vivo cardiac modeling that may be deployed to generate more holistic models of early cardiac morphogenesis, and by extension, new platforms to study congenital heart defects.

Valveless pumping behavior of the simulated embryonic heart tube as a function of contractile patterns and myocardial stiffness

During development, the heart begins pumping as a valveless multilayered tube capable of driving blood flow throughout the embryonic vasculature. The mechanical properties and how they interface with pumping function are not well-defined at this stage. Here, we evaluate pumping patterns using a fluid-structure interaction computational model, combined with experimental data and an energetic analysis to investigate myocardial mechanical properties. Through this work, we propose that a myocardium modeled as a Neo-Hookean material with a material constant on the order of 10 kPa is necessary for the heart tube to function with an optimal pressure and cardiac output.

In Vivo Pressurization of the Zebrafish Embryonic Heart as a Tool to Characterize Tissue Properties During Development

Cardiac morphogenesis requires an intricate orchestration of mechanical stress to sculpt the heart as it transitions from a straight tube to a multichambered adult heart. Mechanical properties are fundamental to this process, involved in a complex interplay with function, morphology, and mechanotransduction. In the current work, we propose a pressurization technique applied to the zebrafish atrium to quantify mechanical properties of the myocardium under passive tension. By further measuring deformation, we obtain a pressure-stretch relationship that is used to identify constitutive models of the zebrafish embryonic cardiac tissue. Two-dimensional results are compared with a three-dimensional finite element analysis based on reconstructed embryonic heart geometry. Through these steps, we found that the myocardium of zebrafish results in a stiffness on the order of 10 kPa immediately after the looping stage of development. This work enables the ability to determine how these properties change under normal and pathological heart development.

Engineering Heart Morphogenesis

Recent advances in stem cell biology and tissue engineering have laid the groundwork for building complex tissues in a dish. We propose that these technologies are ready for a new challenge: recapitulating cardiac morphogenesis in vitro. In development, the heart transforms from a simple linear tube to a four-chambered organ through a complex process called looping. Here, we re-examine heart tube looping through the lens of an engineer and argue that the linear heart tube is an advantageous starting point for tissue engineering. We summarize the structures, signaling pathways, and stresses in the looping heart, and evaluate approaches that could be used to build a linear heart tube and guide it through the process of looping.

Micro-indentation and optical coherence tomography for the mechanical characterization of embryos: Experimental setup and measurements on chicken embryos

The investigation of the mechanical properties of embryos is expected to provide valuable information on the phenomenology of morphogenesis. It is thus believed that, by mapping the viscoelastic features of an embryo at different stages of growth, it may be possible to shed light on the role of mechanics in embryonic development. To contribute to this field, we present a new instrument that can determine spatiotemporal distributions of mechanical properties of embryos over a wide area and with unprecedented accuracy. The method relies on combining ferrule-top micro-indentation, which provides local measurements of viscoelasticity, with Optical Coherence Tomography, which can reveal changes in tissue morphology and help the user identify the indentation point. To prove the working principle, we have collected viscoelasticity maps of fixed and live HH11-HH12 chicken embryos. Our study shows that the instrument can reveal correlations between tissue morphology and mechanical behavior. STATEMENT OF SIGNIFICANCE: Local mechanical properties of soft biological tissue play a crucial role in several biological processes, including cell differentiation, cell migration, and body formation; therefore, measuring tissue properties at high resolution is of great interest in biology and tissue engineering. To provide an efficient method for the biomechanical characterization of soft biological tissues, we introduce a new tool in which the combination of non-invasive Optical Coherence Tomography imaging and depth-controlled indentation measurements allows one to map the viscoelastic properties of biological tissue and investigate correlations between local mechanical features and tissue morphology with unprecedented resolution.

On the Biomechanics of Cardiac S-looping: insights from modeling and perturbation studies

Cardiac looping is an important embryonic developmental stage where the primitive heart tube (HT) twists into a configuration that more closely resembles the mature heart. Improper looping leads to congenital defects. We study cardiac s-looping wherein the primitive ventricle which lay superior to the atrium now assumes its definitive position inferior to it. This process results in a heart loop that is no longer planar with the inflow and outflow tracts now lying in adjacent planes. We investigate the biomechanics of s-looping and use modeling to understand the nonlinear and time variant morphogenetic shape changes. We developed physical and finite element models and validated the models using perturbation studies. The results from experiments and models show how force actuators such as bending of the embryonic dorsal wall (cervical flexure), rotation around the body axis (embryo torsion), and HT growth interact to produce the heart loop. Using model-based and experimental data, we present an improved hypothesis for early cardiac s-looping.

Multiscale analysis of architecture, cell size and the cell cortex reveals cortical F-actin density and composition are major contributors to mechanical properties during convergent extension

The large-scale movements that construct complex three-dimensional tissues during development are governed by universal physical principles. Fine-grained control of both mechanical properties and force production is crucial to the successful placement of tissues and shaping of organs. Embryos of the frog Xenopus laevis provide a dramatic example of these physical processes, as dorsal tissues increase in Young's modulus by six-fold to 80 Pascal over 8 h as germ layers and the central nervous system are formed. These physical changes coincide with emergence of complex anatomical structures, rounds of cell division, and cytoskeletal remodeling. To understand the contribution of these diverse structures, we adopt the cellular solids model to relate bulk stiffness of a solid foam to the unit size of individual cells, their microstructural organization, and their material properties. Our results indicate that large-scale tissue architecture and cell size are not likely to influence the bulk mechanical properties of early embryonic or progenitor tissues but that F-actin cortical density and composition of the F-actin cortex play major roles in regulating the physical mechanics of embryonic multicellular tissues.

Evaluating biomechanical properties of murine embryos using Brillouin microscopy and optical coherence tomography

Embryogenesis is regulated by numerous changes in mechanical properties of the cellular microenvironment. Thus, studying embryonic mechanophysiology can provide a more thorough perspective of embryonic development, potentially improving early detection of congenital abnormalities as well as evaluating and developing therapeutic interventions. A number of methods and techniques have been used to study cellular biomechanical properties during embryogenesis. While some of these techniques are invasive or involve the use of external agents, others are compromised in terms of spatial and temporal resolutions. We propose the use of Brillouin microscopy in combination with optical coherence tomography (OCT) to measure stiffness as well as structural changes in a developing embryo. While Brillouin microscopy assesses the changes in stiffness among different organs of the embryo, OCT provides the necessary structural guidance.

A new hypothesis for foregut and heart tube formation based on differential growth and actomyosin contraction

For decades, it was commonly thought that the bilateral heart fields in the early embryo fold directly towards the midline, where they meet and fuse to create the primitive heart tube. Recent studies have challenged this view, however, suggesting that the heart fields fold diagonally. As early foregut and heart tube morphogenesis are intimately related, this finding also raises questions concerning the traditional view of foregut formation. Here, we combine experiments on chick embryos with computational modeling to explore a new hypothesis for the physical mechanisms of heart tube and foregut formation. According to our hypothesis, differential anisotropic growth between mesoderm and endoderm drives diagonal folding. Then, active contraction along the anterior intestinal portal generates tension to elongate the foregut and heart tube. We test this hypothesis using biochemical perturbations of cell proliferation and contractility, as well as computational modeling based on nonlinear elasticity theory including growth and contraction. The present results generally support the view that differential growth and actomyosin contraction drive formation of the foregut and heart tube in the early chick embryo.

A toolbox to explore the mechanics of living embryonic tissues

The sculpting of embryonic tissues and organs into their functional morphologies involves the spatial and temporal regulation of mechanics at cell and tissue scales. Decades of in vitro work, complemented by some in vivo studies, have shown the relevance of mechanical cues in the control of cell behaviors that are central to developmental processes, but the lack of methodologies enabling precise, quantitative measurements of mechanical cues in vivo have hindered our understanding of the role of mechanics in embryonic development. Several methodologies are starting to enable quantitative studies of mechanics in vivo and in situ, opening new avenues to explore how mechanics contributes to shaping embryonic tissues and how it affects cell behavior within developing embryos. Here we review the present methodologies to study the role of mechanics in living embryonic tissues, considering their strengths and drawbacks as well as the conditions in which they are most suitable.

Discrete Element Framework for Modelling Extracellular Matrix, Deformable Cells and Subcellular Components

This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus) and extracellular matrix (e.g. collagen) are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties). Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings). Each particle is in effect an ‘agent’, meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory.

Modelling is an important tool in understanding the behaviour of biological tissues. In this paper we advocate a new modelling framework in which cells and tissues are represented by a collection of particles with associated properties. The particles interact with each other and can change their behaviour in response to changes in their environment. We demonstrate how the propose framework can be used to represent the mechanical behaviour of different tissues with much greater flexibility as compared to traditional continuum based methods.

Dimensionless analysis of valveless pumping in a thick-wall elastic tube: Application to the tubular embryonic heart

The physical mechanism that drives blood flow in the valveless tubular embryonic heart is still debatable whether it is peristaltic flow or valveless dynamic suction. Previous studies of valveless pumping were concerned with either the role of the excitation parameters or the mechanisms that generate the unidirectional outflow. In this study, a dimensionless one-dimensional (1D) analysis of the valveless pumping due to local excitation at an asymmetric longitudinal location was performed for non-uniform thick-wall elastic tubes, including tubes with local bulging and tapering. A general tube law that accounts for wall thicknesses was implemented for describing the physically realistic dynamics of the tube and the two-step MacCormack algorithm was utilized for the numerical analysis. A comprehensive analysis was conducted to explore the affecting roles of the system (e.g., tube geometry) and the working (e.g., Strouhal number and flow friction parameter) parameters on the net outflow of the pump. The maximal positive net outflow in all the tested cases always occurred when the natural Strouhal number was about π. Flow reversals were observed only for relatively low friction parameters. A local bulging at the site of excitation and thick walls contributed to larger outflows, while tube tapering reduced the net outflow.

Why is cytoskeletal contraction required for cardiac fusion before but not after looping begins?

Cytoskeletal contraction is crucial to numerous morphogenetic processes, but its role in early heart development is poorly understood. Studies in chick embryos have shown that inhibiting myosin-II-based contraction prior to Hamburger-Hamilton (HH) stage 10 (33 h incubation) impedes fusion of the mesodermal heart fields that create the primitive heart tube (HT), as well as the ensuing process of cardiac looping. If contraction is inhibited at or after looping begins at HH10, however, fusion and looping proceed relatively normally. To explore the mechanisms behind this seemingly fundamental change in behavior, we measured spatiotemporal distributions of tissue stiffness, stress, and strain around the anterior intestinal portal (AIP), the opening to the foregut where contraction and cardiac fusion occur. The results indicate that stiffness and tangential tension decreased bilaterally along the AIP with distance from the embryonic midline. The gradients in stiffness and tension, as well as strain rate, increased to peaks at HH9 (30 h) and decreased afterward. Exposure to the myosin II inhibitor blebbistatin reduced these effects, suggesting that they are mainly generated by active cytoskeletal contraction, and finite-element modeling indicates that the measured mechanical gradients are consistent with a relatively uniform contraction of the endodermal layer in conjunction with constraints imposed by the attached mesoderm. Taken together, our results suggest that, before HH10, endodermal contraction pulls the bilateral heart fields toward the midline where they fuse to create the HT. By HH10, however, the fusion process is far enough along to enable apposing cardiac progenitor cells to keep 'zipping' together during looping without the need for continued high contractile forces. These findings should shed new light on a perplexing question in early heart development.

Bending of the looping heart: differential growth revisited

In the early embryo, the primitive heart tube (HT) undergoes the morphogenetic process of c-looping as it bends and twists into a c-shaped tube. Despite intensive study for nearly a century, the physical forces that drive looping remain poorly understood. This is especially true for the bending component, which is the focus of this paper. For decades, experimental measurements of mitotic rates had seemingly eliminated differential growth as the cause of HT bending, as it has commonly been thought that the heart grows almost exclusively via hyperplasia before birth and hypertrophy after birth. Recently published data, however, suggests that hypertrophic growth may play a role in looping. To test this idea, we developed finite-element models that include regionally measured changes in myocardial volume over the HT. First, models based on idealized cylindrical geometry were used to simulate the bending process in isolated hearts, which bend without the complicating effects of external loads. With the number of free parameters in the model reduced to the extent possible, stress and strain distributions were compared to those measured in embryonic chick hearts that were isolated and cultured for 24 h. The results show that differential growth alone yields results that agree reasonably well with the trends in our data, but adding active changes in myocardial cell shape provides closer quantitative agreement with stress measurements. Next, the estimated parameters were extrapolated to a model based on realistic 3D geometry reconstructed from images of an actual chick heart. This model yields similar results and captures quite well the basic morphology of the looped heart. Overall, our study suggests that differential hypertrophic growth in the myocardium (MY) is the primary cause of the bending component of c-looping, with other mechanisms possibly playing lesser roles.

Probing regional mechanical properties of embryonic tissue using microindentation and optical coherence tomography

Physical forces regulate morphogenetic movements and the mechanical properties of embryonic tissues during development. Such quantities are closely interrelated, as increases in material stiffness can limit force-induced deformations and vice versa. Here we present a minimally invasive method to quantify spatiotemporal changes in mechanical properties during morphogenesis. Regional stiffness is measured using microindentation, while displacement and strain distributions near the indenter are computed from the motion of tissue labels tracked from 3-D optical coherence tomography (OCT) images. Applied forces, displacements, and strain distributions are then used in conjunction with finite-element models to estimate regional material properties. This method is applicable to a wide variety of experimental systems and can be used to better understand the dynamic interrelation between tissue deformations and material properties that occur during time-lapse studies of embryogenesis. Such information is important to improve our understanding of the etiology of congenital disease where dynamic changes in mechanical properties are likely involved, such as situs inversus in the heart, hydrocephalus in the brain, and microphthalmia in the eye.

Elasticity-based targeted growth models of morphogenesis

Embryonic tissue mechanics play an important role in regulating morphogenesis during organ formation, both in a bottom-up sense, where changes in gene expression drive mechanical shape changes, and in a top-down sense, where perturbations in tissue mechanics feed back to drive changes in gene expression. In growing tissues that can generate internal forces and have complex geometries, like those in the embryo, it can often be difficult to empirically determine the mechanical state of the tissue, let alone the relationships between gene expression and mechanical behavior. Mathematical models can be used to fill this gap. Here, we discuss elasticity-based models for growing tissues with a specific focus on targeted growth in embryonic tissues.

Mechanosensitive kinases regulate stiffness-induced cardiomyocyte maturation

Cells secrete and assemble extracellular matrix throughout development, giving rise to time-dependent, tissue-specific stiffness. Mimicking myocardial matrix stiffening, i.e. ~10-fold increase over 1 week, with a hydrogel system enhances myofibrillar organization of embryonic cardiomyocytes compared to static hydrogels, and thus we sought to identify specific mechanosensitive proteins involved. Expression and/or phosphorylation state of 309 unique protein kinases were examined in embryonic cardiomyocytes plated on either dynamically stiffening or static mature myocardial stiffness hydrogels. Gene ontology analysis of these kinases identified cardiogenic pathways that exhibited time-dependent up-regulation on dynamic versus static matrices, including PI3K/AKT and p38 MAPK, while GSK3β, a known antagonist of cardiomyocyte maturation, was down-regulated. Additionally, inhibiting GSK3β on static matrices improved spontaneous contraction and myofibril organization, while inhibiting agonist AKT on dynamic matrices reduced myofibril organization and spontaneous contraction, confirming its role in mechanically-driven maturation. Together, these data indicate that mechanically-driven maturation is at least partially achieved via active mechanosensing at focal adhesions, affecting expression and phosphorylation of a variety of protein kinases important to cardiomyogenesis.

Bending and twisting the embryonic heart: a computational model for c-looping based on realistic geometry

The morphogenetic process of cardiac looping transforms the straight heart tube into a curved tube that resembles the shape of the future four-chambered heart. Although great progress has been made in identifying the molecular and genetic factors involved in looping, the physical mechanisms that drive this process have remained poorly understood. Recent work, however, has shed new light on this complicated problem. After briefly reviewing the current state of knowledge, we propose a relatively comprehensive hypothesis for the mechanics of the first phase of looping, termed c-looping, as the straight heart tube deforms into a c-shaped tube. According to this hypothesis, differential hypertrophic growth in the myocardium supplies the main forces that cause the heart tube to bend ventrally, while regional growth and cytoskeletal contraction in the omphalomesenteric veins (primitive atria) and compressive loads exerted by the splanchnopleuric membrane drive rightward torsion. A computational model based on realistic embryonic heart geometry is used to test the physical plausibility of this hypothesis. The behavior of the model is in reasonable agreement with available experimental data from control and perturbed embryos, offering support for our hypothesis. The results also suggest, however, that several other mechanisms contribute secondarily to normal looping, and we speculate that these mechanisms play backup roles when looping is perturbed. Finally, some outstanding questions are discussed for future study.

Augmentation of integrin-mediated mechanotransduction by hyaluronic acid

Changes in tissue and organ stiffness occur during development and are frequently symptoms of disease. Many cell types respond to the stiffness of substrates and neighboring cells in vitro and most cell types increase adherent area on stiffer substrates that are coated with ligands for integrins or cadherins. In vivo cells engage their extracellular matrix (ECM) by multiple mechanosensitive adhesion complexes and other surface receptors that potentially modify the mechanical signals transduced at the cell/ECM interface. Here we show that hyaluronic acid (also called hyaluronan or HA), a soft polymeric glycosaminoglycan matrix component prominent in embryonic tissue and upregulated during multiple pathologic states, augments or overrides mechanical signaling by some classes of integrins to produce a cellular phenotype otherwise observed only on very rigid substrates. The spread morphology of cells on soft HA-fibronectin coated substrates, characterized by formation of large actin bundles resembling stress fibers and large focal adhesions resembles that of cells on rigid substrates, but is activated by different signals and does not require or cause activation of the transcriptional regulator YAP. The fact that HA production is tightly regulated during development and injury and frequently upregulated in cancers characterized by uncontrolled growth and cell movement suggests that the interaction of signaling between HA receptors and specific integrins might be an important element in mechanical control of development and homeostasis.

The interplay between cell signalling and mechanics in developmental processes

Force production and the propagation of stress and strain within embryos and organisms are crucial physical processes that direct morphogenesis. In addition, there is mounting evidence that biomechanical cues created by these processes guide cell behaviours and cell fates. In this Review we discuss key roles for biomechanics during development to directly shape tissues, to provide positional information for cell fate decisions and to enable robust programmes of development. Several recently identified molecular mechanisms suggest how cells and tissues might coordinate their responses to biomechanical cues. Finally, we outline long-term challenges in integrating biomechanics with genetic analysis of developing embryos.

Computational and experimental study of the mechanics of embryonic wound healing

Wounds in the embryo show a remarkable ability to heal quickly without leaving a scar. Previous studies have found that an actomyosin ring (purse string) forms around the wound perimeter and contracts to close the wound over the course of several dozens of minutes. Here, we report experiments that reveal an even faster mechanism which remarkably closes wounds by more than 50% within the first 30s. Circular and elliptical wounds (~100μm in size) were made in the blastoderm of early chick embryos and allowed to heal, with wound area and shape characterized as functions of time. The closure rate displayed a biphasic behavior, with rapid constriction lasting about a minute, followed by a period of more gradual closure to complete healing. Fluorescent staining suggests that both healing phases are driven by actomyosin contraction, with relatively rapid contraction of fibers at cell borders within a relatively thick ring of tissue (several cells wide) around the wound followed by slower contraction of a thin supracellular actomyosin ring along the margin, consistent with a purse string mechanism. Finite-element modeling showed that this idea is biophysically plausible, with relatively isotropic contraction within the thick ring giving way to tangential contraction in the thin ring. In addition, consistent with experimental results, simulated elliptical wounds heal with little change in aspect ratio, and decreased membrane tension can cause these wounds to open briefly before going on to heal. These results provide new insight into the healing mechanism in embryonic epithelia.

On the role of intrinsic and extrinsic forces in early cardiac S-looping

BACKGROUND

Looping is a crucial phase during heart development when the initially straight heart tube is transformed into a shape that more closely resembles the mature heart. Although the genetic and biochemical pathways of cardiac looping have been well studied, the biophysical mechanisms that actually effect the looping process remain poorly understood. Using a combined experimental (chick embryo) and computational (finite element modeling) approach, we study the forces driving early s-looping when the primitive ventricle moves to its definitive position inferior to the common atrium.

RESULTS

New results from our study indicate that the primitive heart has no intrinsic ability to form an s-loop and that extrinsic forces are necessary to effect early s-looping. They support previous studies that established an important role for cervical flexure in causing early cardiac s-looping. Our results also show that forces applied by the splanchnopleure cannot be ignored during early s-looping and shed light on the role of cardiac jelly. Using available experimental data and computer modeling, we successfully developed and tested a hypothesis for the force mechanisms driving s-loop formation.

CONCLUSIONS

Forces external to the primitive heart tube are necessary in the later stages of cardiac looping. Experimental and model results support our proposed hypothesis for forces driving early s-looping.

Viscoelastic material properties of the myocardium and cardiac jelly in the looping chick heart

Accurate material properties of developing embryonic tissues are a crucial factor in studies of the mechanics of morphogenesis. In the present work, we characterize the viscoelastic material properties of the looping heart tube in the chick embryo through nonlinear finite element modeling and microindentation experiments. Both hysteresis and ramp-hold experiments were performed on the intact heart and isolated cardiac jelly (extracellular matrix). An inverse computational method was used to determine the constitutive relations for the myocardium and cardiac jelly. With both layers assumed to be quasilinear viscoelastic, material coefficients for an Ogden type strain-energy density function combined with Prony series of two terms or less were determined by fitting numerical results from a simplified model of a heart segment to experimental data. The experimental and modeling techniques can be applied generally for determining viscoelastic material properties of embryonic tissues.

Embryo mechanics: balancing force production with elastic resistance during morphogenesis

Morphogenesis requires the spatial and temporal control of embryo mechanics, including force production and mechanical resistance to those forces, to coordinate tissue deformation and large-scale movements. Thus, biomechanical processes play a key role in directly shaping the embryo. Additional roles for embryo mechanics during development may include the patterning of positional information and to provide feedback to ensure the success of morphogenetic movements in shaping the larval body and organs. To understand the multiple roles of mechanics during development requires familiarity with engineering principles of the mechanics of structures, the viscoelastic properties of biomaterials, and the integration of force and stress within embryonic structures as morphogenesis progresses. In this chapter, we review the basic engineering principles of biomechanics as they relate to morphogenesis, introduce methods for quantifying embryo mechanics and the limitations of these methods, and outline a formalism for investigating the role of embryo mechanics in birth defects. We encourage the nascent field of embryo mechanics to adopt standard engineering terms and test methods so that studies of diverse organisms can be compared and universal biomechanical principles can be revealed.

Surprisingly simple mechanical behavior of a complex embryonic tissue

BACKGROUND

Previous studies suggest that mechanical feedback could coordinate morphogenetic events in embryos. Furthermore, embryonic tissues have complex structure and composition and undergo large deformations during morphogenesis. Hence we expect highly non-linear and loading-rate dependent tissue mechanical properties in embryos.

METHODOLOGY/PRINCIPAL FINDINGS

We used micro-aspiration to test whether a simple linear viscoelastic model was sufficient to describe the mechanical behavior of gastrula stage Xenopus laevis embryonic tissue in vivo. We tested whether these embryonic tissues change their mechanical properties in response to mechanical stimuli but found no evidence of changes in the viscoelastic properties of the tissue in response to stress or stress application rate. We used this model to test hypotheses about the pattern of force generation during electrically induced tissue contractions. The dependence of contractions on suction pressure was most consistent with apical tension, and was inconsistent with isotropic contraction. Finally, stiffer clutches generated stronger contractions, suggesting that force generation and stiffness may be coupled in the embryo.

CONCLUSIONS/SIGNIFICANCE

The mechanical behavior of a complex, active embryonic tissue can be surprisingly well described by a simple linear viscoelastic model with power law creep compliance, even at high deformations. We found no evidence of mechanical feedback in this system. Together these results show that very simple mechanical models can be useful in describing embryo mechanics.

The mechanics of development: Models and methods for tissue morphogenesis

Embryonic development is a physical process during which groups of cells are sculpted into functional organs. The mechanical properties of tissues and the forces exerted on them serve as epigenetic regulators of morphogenesis. Understanding these mechanobiological effects in the embryo requires new experimental approaches. Here we focus on branching of the lung airways and bending of the heart tube to describe examples of mechanical and physical cues that guide cell fate decisions and organogenesis. We highlight recent technological advances to measure tissue elasticity and endogenous mechanical stresses in real time during organ development. We also discuss recent progress in manipulating forces in intact embryos.

Mechanics of head fold formation: investigating tissue-level forces during early development

During its earliest stages, the avian embryo is approximately planar. Through a complex series of folds, this flat geometry is transformed into the intricate three-dimensional structure of the developing organism. Formation of the head fold (HF) is the first step in this cascading sequence of out-of-plane tissue folds. The HF establishes the anterior extent of the embryo and initiates heart, foregut and brain development. Here, we use a combination of computational modeling and experiments to determine the physical forces that drive HF formation. Using chick embryos cultured ex ovo, we measured: (1) changes in tissue morphology in living embryos using optical coherence tomography (OCT); (2) morphogenetic strains (deformations) through the tracking of tissue labels; and (3) regional tissue stresses using changes in the geometry of circular wounds punched through the blastoderm. To determine the physical mechanisms that generate the HF, we created a three-dimensional computational model of the early embryo, consisting of pseudoelastic plates representing the blastoderm and vitelline membrane. Based on previous experimental findings, we simulated the following morphogenetic mechanisms: (1) convergent extension in the neural plate (NP); (2) cell wedging along the anterior NP border; and (3) autonomous in-plane deformations outside the NP. Our numerical predictions agree relatively well with the observed morphology, as well as with our measured stress and strain distributions. The model also predicts the abnormal tissue geometries produced when development is mechanically perturbed. Taken together, the results suggest that the proposed morphogenetic mechanisms provide the main tissue-level forces that drive HF formation.

Axons pull on the brain, but tension does not drive cortical folding

During human brain development, the cerebral cortex undergoes substantial folding, leading to its characteristic highly convoluted form. Folding is necessary to accommodate the expansion of the cerebral cortex; abnormal cortical folding is linked to various neurological disorders, including schizophrenia, epilepsy, autism, and mental retardation. Although this process requires mechanical forces, the specific force-generating mechanisms that drive folding remain unclear. The two most widely accepted hypotheses are as follows: (1) Folding is caused by differential growth of the cortex and (2) folding is caused by mechanical tension generated in axons. Direct evidence supporting either theory, however, is lacking. Here we show that axons are indeed under considerable tension in the developing ferret brain, but the patterns of tissue stress are not consistent with a causal role for axonal tension. In particular, microdissection assays reveal that significant tension exists along axons aligned circumferentially in subcortical white matter tracts, as well as those aligned radially inside developing gyri (outward folds). Contrary to previous speculation, however, axonal tension is not directed across developing gyri, suggesting that axon tension does not drive folding. On the other hand, using computational (finite element) models, we show that differential cortical growth accompanied by remodeling of the subplate leads to outward folds and stress fields that are consistent with our microdissection experiments, supporting a mechanism involving differential growth. Local perturbations, such as temporal differences in the initiation of cortical growth, can ensure consistent folding patterns. This study shows that a combination of experimental and computational mechanics can be used to evaluate competing hypotheses of morphogenesis, and illuminate the biomechanics of cortical folding.

Opening angles and material properties of the early embryonic chick brain

Mechanical forces play an important role during brain development. In the early embryo, the anterior end of the neural tube enlarges and differentiates into the major brain subdivisions, including three expanding vesicles (forebrain, midbrain, and hindbrain) separated by two constrictions. Once the anterior neuropore and the spinal neurocoel occlude, the brain tube undergoes further regional growth and expansion in response to increasing cerebrospinal fluid pressure. Although this is known to be a response to mechanical loads, the mechanical properties of the developing brain remain largely unknown. In this work, we measured regional opening angles (due to residual stress) and stiffness of the embryonic chick brain during Hamburger-Hamilton stages 11-13 (approximately 42-51 h incubation). Opening angles resulting from a radial cut on transverse brain slices were about 40-110 deg (depending on region and stage) and served as an indicator of circumferential residual stress. In addition, using a custom-made microindentation device and finite-element models, we determined regional indentation stiffness and material properties. The results indicate that the modulus is relatively independent of position and stage of development with the average shear modulus being about 220 Pa for stages 11-13 chick brains. Information on the regional material properties of the early embryonic brain will help illuminate the process of early brain morphogenesis.

The role of mechanical forces in the torsional component of cardiac looping

During early development, the initially straight heart tube (HT) bends and twists (loops) into a curved tube to lay out the basic plan of the mature heart. The physical mechanisms that drive and regulate looping are not yet completely understood. This paper reviews our recent studies of the mechanics of cardiac torsion during the first phase of looping (c-looping). Experiments and computational modeling show that torsion is primarily caused by forces exerted on the HT by the primitive atria and the splanchnopleure, a membrane that presses against the ventral surface of the heart. Experimental and numerical results are described and integrated to propose a hypothesis for cardiac torsion, and key aspects of our hypothesis are tested using experiments that perturb normal looping. For each perturbation, the models predict the correct qualitative response. These studies provide new insight into the mechanisms that drive and regulate cardiac looping.

Multi-scale mechanics from molecules to morphogenesis

Dynamic mechanical processes shape the embryo and organs during development. Little is understood about the basic physics of these processes, what forces are generated, or how tissues resist or guide those forces during morphogenesis. This review offers an outline of some of the basic principles of biomechanics, provides working examples of biomechanical analyses of developing embryos, and reviews the role of structural proteins in establishing and maintaining the mechanical properties of embryonic tissues. Drawing on examples we highlight the importance of investigating mechanics at multiple scales from milliseconds to hours and from individual molecules to whole embryos. Lastly, we pose a series of questions that will need to be addressed if we are to understand the larger integration of molecular and physical mechanical processes during morphogenesis and organogenesis.

On modeling morphogenesis of the looping heart following mechanical perturbations

Looping is a crucial early phase during heart development, as the initially straight heart tube (HT) deforms into a curved tube to lay out the basic plan of the mature heart. This paper focuses on the first phase of looping, called c-looping, when the HT bends ventrally and twists dextrally (rightward) to create a c-shaped tube. Previous research has shown that bending is an intrinsic process, while dextral torsion is likely caused by external forces acting on the heart. However, the specific mechanisms that drive and regulate looping are not yet completely understood. Here, we present new experimental data and finite element models to help define these mechanisms for the torsional component of c-looping. First, with regions of growth and contraction specified according to experiments on chick embryos, a three-dimensional model exhibits morphogenetic deformation consistent with observations for normal looping. Next, the model is tested further using experiments in which looping is perturbed by removing structures that exert forces on the heart--a membrane (splanchnopleure (SPL)) that presses against the ventral surface of the heart and the left and right primitive atria. In all cases, the model predicts the correct qualitative behavior. Finally, a two-dimensional model of the HT cross section is used to study a feedback mechanism for stress-based regulation of looping. The model is tested using experiments in which the SPL is removed before, during, and after c-looping. In each simulation, the model predicts the correct response. Hence, these models provide new insight into the mechanical mechanisms that drive and regulate cardiac looping.

Actomyosin stiffens the vertebrate embryo during crucial stages of elongation and neural tube closure

Physical forces drive the movement of tissues within the early embryo. Classical and modern approaches have been used to infer and, in rare cases, measure mechanical properties and the location and magnitude of forces within embryos. Elongation of the dorsal axis is a crucial event in early vertebrate development, yet the mechanics of dorsal tissues in driving embryonic elongation that later support neural tube closure and formation of the central nervous system is not known. Among vertebrates, amphibian embryos allow complex physical manipulation of embryonic tissues that are required to measure the mechanical properties of tissues. In this paper, we measure the stiffness of dorsal isolate explants of frog (Xenopus laevis) from gastrulation to neurulation and find dorsal tissues stiffen from less than 20 Pascal (Pa) to over 80 Pa. By iteratively removing tissues from these explants, we find paraxial somitic mesoderm is nearly twice as stiff as either the notochord or neural plate, and at least 10-fold stiffer than the endoderm. Stiffness measurements from explants with reduced fibronectin fibril assembly or disrupted actomyosin contractility suggest that it is the state of the actomyosin cell cortex rather than accumulating fibronectin that controls tissue stiffness in early amphibian embryos.

Natural variation in embryo mechanics: gastrulation in Xenopus laevis is highly robust to variation in tissue stiffness

How sensitive is morphogenesis to the mechanical properties of embryos? To estimate an upper bound on the sensitivity of early morphogenetic movements to tissue mechanical properties, we assessed natural variability in the apparent stiffness among gastrula-stage Xenopus laevis embryos. We adapted micro-aspiration methods to make repeated, nondestructive measurements of apparent tissue stiffness in whole embryos. Stiffness varied by close to a factor of 2 among embryos within a single clutch. Variation between clutches was of similar magnitude. On the other hand, the direction of change in stiffness over the course of gastrulation was the same in all embryos and in all clutches. Neither pH nor salinity--two environmental factors we predicted could affect variability in nature--affected tissue stiffness. Our results indicate that gastrulation in X. laevis is robust to at least twofold variation in tissue stiffness.

Variation and robustness of the mechanics of gastrulation: the role of tissue mechanical properties during morphogenesis

Diverse mechanisms of morphogenesis generate a wide variety of animal forms. In this work, we discuss two ways that the mechanical properties of embryonic tissues could guide one of the earliest morphogenetic movements in animals, gastrulation. First, morphogenetic movements are a function of both the forces generated by cells and the mechanical properties of the tissues. Second, cells could change their behavior in response to their mechanical environment. Theoretical studies of gastrulation indicate that different morphogenetic mechanisms differ in their inherent sensitivity to tissue mechanical properties. Those few empirical studies that have investigated the mechanical properties of amphibian and echinoderm gastrula-stage embryos indicate that there could be high embryo-to-embryo variability in tissue stiffness. Such high embryo-to-embryo variability would imply that gastrulation is fairly robust to variation in tissue stiffness. Cell culture studies demonstrate a wide variety of cellular responses to the mechanical properties of their microenvironment. These responses are likely to be developmentally regulated, and could either increase or decrease the robustness of gastrulation movements depending on which cells express which responses. Hence both passive physical and mechanoregulatory processes will determine how sensitive gastrulation is to tissue mechanics. Addressing these questions is important for understanding the significance of diverse programs of early development, and how genetic or environmental perturbations influence development. We discuss methods for measuring embryo-to-embryo variability in tissue mechanics, and for experimentally perturbing those mechanical properties to determine the sensitivity of gastrulation to tissue mechanics.